Related papers: Chaotic behaviour on invariant sets of linear oper…
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence,…
We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate…
This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relation to invariant continua. These…
In this paper, we study distributional chaos for weighted translations on locally compact groups. We give a sufficient condition for such operators to be distributionally chaotic and construct an example of distributionally chaotic weighted…
The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In…
It is well-known that the action of a hyperbolic element (``cat map'') of the modular group on the 2-torus has strong chaotic dynamical properties such as mixing and exponential decay of correlations. In this note we study stability of this…
We introduce several different notions of disjoint distributional chaos for sequences of multivalued linear operators in Fr\'echet spaces. Any of these notions seems to be new and not considered elsewhere even for linear continuous…
Let $X$ be a complex topological vector space with dim$(X)>1$ and $\mathcal{B}(X)$ the space of all continuous linear operators on $X$. In this paper, we extend the concept of supercyclicity of a single operators and strongly continuous…
We study different pointwise recurrence notions for linear dynamical systems from the Ergodic Theory point of view. We show that from any reiteratively recurrent vector $x_0$, for an adjoint operator $T$ on a separable dual Banach space…
In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved…
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
Recently, it was shown that certain systems with large time-varying delay exhibit different types of chaos, which are related to two types of time-varying delay: conservative and dissipative delays. The known high-dimensional Turbulent…
We investigate the harmonic analysis associated with the hyper-Bessel operator on C, and we prove the chaotic character of the related convolution operators.
The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic)…
Chaos as typical property of non-linear systems has revealed its crucial role in various problems of astrophysics and cosmology. The problems discussed at these lectures include planetary dynamics, galactic dynamics, reconstruction of the…
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…